On a certain result of Z. Opial

On certain integral inequalities related to Opial's inequality

“…Moreover, Olech showed that (1) is valid for any function [(x) which is absolutely continuous on [0, b] and satisfies the boundary conditions [(0) ----fib) = 0. Our results in the special cases yield the well known Opi~l inequality (1) and some of its generalizations given by Yang [6]. In the present paper we establish some new integral inequalities similar to Opial's inequality involving three functions and their derivatives.…”

“…Since then a large number of papers have been appeared in the literature which deals with the simpler proofs and various generalizations of OpiM's inequality, see for example [2] (p. 154--162), [5] and the references given therein. The following inequalities analogues to Theorem 1 also yield in the special cases the Opial inequality (1) and some of its generalizations given by Yang in [6]. Our results in the special cases yield the well known Opi~l inequality (1) and some of its generalizations given by Yang [6].…”

Dynamic Inequalities On Time Scales

“…Remark 3.1.1 Note that in the case when T = R, the inequality (3.1.20) reduces to the Yang [152] inequality…”

On integral inequalities similar to Opial's inequality

“…The proof of (2) is similar in the aa8e of u(b) = v(b) = 0. This completes the proof of Theorem 1* In order to prove Theorem 2, we first observe that having b J p(x)dx » 1, by assumption, we can write a ) / Hftf 1 (12) …”